Homogenization of Discrete High-Contrast Energies

Variational theories of double-porosity models can be derived by homogenization of high-contrast periodic media (see [12]). Typically, we have one or more strong phases (i.e., uniformly elliptic energies on periodic connected domains) and a weak phase with a small ellipticity constant, coupled with some lower-order term. In the simplest case of quadratic energies, this amounts to considering energies of the form